Answer to Question #166833 in Statistics and Probability for Ivy Grace

Question #166833

the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?


1
Expert's answer
2021-02-26T01:03:39-0500

Having a normal distribution with parameters "\\mu" = 55 and "\\sigma" = 9 we need to find the time T: P(t < T) = 0.92 . The same is to find T' = (T - "\\mu") / "\\sigma" , which is the 0.92 quantile of normal distribution with parameters "\\mu" = 0 and "\\sigma" = 1. So T' = 1.41 and T = "\\sigma" *T' + "\\mu" = 9*1.41 + 55 = 67.69.. The test should  be terminated after 67.7 minutes.


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